To solve the given expression and write the result in scientific notation, let's start by breaking down the calculations step by step.
### Step 1: Understanding the Expression
The expression we need to solve is given as:
[tex]\[
\frac{\left(8 \times 10^2\right)\left(3.2 \times 10^5\right)}{4 \times 10^3}
\][/tex]
### Step 2: Multiplying the Numerator
First, let's multiply the terms in the numerator:
[tex]\[
(8 \times 10^2) \times (3.2 \times 10^5)
\][/tex]
Separate the numerical coefficients and powers of 10:
[tex]\[
8 \times 3.2 = 25.6
\][/tex]
[tex]\[
10^2 \times 10^5 = 10^{2+5} = 10^7
\][/tex]
Thus, the product of the numerator is:
[tex]\[
25.6 \times 10^7
\][/tex]
### Step 3: Dividing by the Denominator
Now, we divide the result from the numerator by the denominator:
[tex]\[
\frac{25.6 \times 10^7}{4 \times 10^3}
\][/tex]
Separate the numerical coefficients and powers of 10 for division:
[tex]\[
\frac{25.6}{4} = 6.4
\][/tex]
[tex]\[
\frac{10^7}{10^3} = 10^{7-3} = 10^4
\][/tex]
Thus, the result of the division is:
[tex]\[
6.4 \times 10^4
\][/tex]
### Step 4: Conclusion
The given mathematical expression simplifies to:
[tex]\[
6.4 \times 10^4
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{6.4 \times 10^4}
\][/tex]
